The lessons linked above give systematic techniques to factor
certain types of polynomials. In practice, solving equations using
factoring often requires the use of a more complex process called
"Factoring Completely". This lesson explains how to factor
completely by combining the three basic techniques listed above.

First, lets take a closer look at why we need the Factoring
Completely process. Examine the expression below:

But notice that this expression is not the same as the factored
expression that we started with. We need another step to factor
this into the expression that we started with. This is where
Factoring Completely comes in.